Polishing composition and polishing method

ABSTRACT

A polishing composition contains silicon dioxide, an alkaline compound, and water. Silicon dioxide is, for example, colloidal silica, fumed silica, or precipitated silica. The alkaline compound is, for example, ammonium carbonate, potassium carbonate, sodium carbonate, ammonium hydrogen carbonate, potassium hydrogen carbonate, sodium hydrogen carbonate, ammonium phosphate, potassium phosphate, sodium phosphate, ammonium hydrogen phosphate, potassium hydrogen phosphate, or sodium hydrogen phosphate. The polishing composition can be suitably used in applications for polishing a glass substrate.

BACKGROUND OF THE INVENTION

The present invention relates to a polishing composition for use in polishing of a glass substrate for an information-recording medium, which is used for a hard disk and the like. The present invention also relates to a polishing method using such a polishing composition.

Conventionally, there is a known polishing composition for use in applications for polishing a glass substrate for an information-recording medium. Japanese Laid-Open Patent Publication No. 2001-89748 discloses a polishing composition (hereinafter referred to as the first prior art polishing composition) containing an abrasive mainly composed of a rare earth oxide such as cerium oxide, and water. Japanese Laid-Open Patent Publication No. 2000-144112 discloses a polishing composition (hereinafter referred to as the second prior art polishing composition) containing an abrasive that comprises at least one selected from the group consisting of an iron-containing oxide and an iron-containing basic compound, and water. These first and second prior art polishing compositions mechanically polish a glass substrate by the action of the abrasive.

Requirements to be met by a polishing composition for use in applications for polishing a glass substrate include:

(1) the surface roughness of the polished glass substrate must be small;

(2) the polishing composition is easy to clean off, namely, the polishing composition is easily removed by cleaning from the glass substrate;

(3) the abrasive has good dispersibility in the polishing composition; and

(4) the polishing composition has a high stock removal rate, i.e., the polishing composition is highly capable of polishing a glass substrate.

The first and second prior art polishing compositions, however, do not satisfy the above requirements, and are thus susceptible to improvement.

SUMMARY OF THE INVENTION

Accordingly, an object of the present invention is to provide a polishing composition that can be suitably used in applications for polishing a glass substrate. Another object of the present invention is to provide a polishing method using such a polishing composition.

To achieve the foregoing and other objectives and in accordance with the purpose of the present invention, the invention provides a polishing composition for use in applications for polishing a glass substrate. The polishing composition contains silicon dioxide, an alkaline compound, and water.

The invention also provides a method for polishing a glass substrate. The method includes preparing the above polishing composition and polishing the surface of a glass substrate, using the prepared polishing composition.

Other aspects and advantages of the invention will become apparent from the following description, illustrating by way of example the principles of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

One embodiment of the present invention will now be described.

A glass substrate for an information-recording medium, such as a magnetic disc, is formed of, for example, aluminosilicate glass, soda lime glass, soda aluminosilicate glass, almino borosilicate glass, borosilicate glass, quartz glass, or crystallized glass. The main crystal phase of the crystallized glass may be spodumene, mullite, aluminum borate crystal, β-quartz solid solution, α-quartz, cordierite, enstatite, celsian, wollastonite, anorthite, forsterite, lithium metasilicate, or lithium disilicate. A glass substrate is usually provided to a chemical machine polishing (CMP) process so as to have the surface thereof mirror-finished.

Typically, the process of polishing a glass substrate is divided into a plurality of polishing steps to be conducted, for the purpose of improving the stock removal rate, as well as the quality of the surface of the polished glass substrate. The plurality of polishing steps include, for example, a step of roughly polishing the glass substrate surface and a step of superfinely polishing the glass substrate surface. In other words, the plurality of polishing steps include, for example, a step of preliminarily polishing the glass substrate surface and a step of finish-polishing the glass substrate surface. A polishing composition according the present embodiment is used, for example, in the final polishing step (finish-polishing step) among the plurality of polishing steps. The polished glass substrate is usually subjected to a chemical strengthening process using a low-temperature ion exchange method or the like, in order to improve resistance to shock and vibration.

The polishing composition according to the present embodiment contains silicon dioxide, an alkaline compound, and water.

Silicon dioxide serves as an abrasive for mechanically polishing a glass substrate. Silicon dioxide may be colloidal silica, fumed silica, or precipitated silica. Among them, colloidal silica or fumed silica is preferable as being capable of reducing the surface roughness of a polished glass substrate, and colloidal silica is more preferable. One or more kinds of silicon dioxide may be contained in the polishing composition.

When silicon dioxide is colloidal silica, the mean particle diameter D_(SA) of colloidal silica, which is determined from the specific surface area thereof by the BET method, is preferably in the range of 5 to 300 nm, more preferably in the range of 5 to 200 nm, and most preferably in the range of 5 to 120 nm. The mean particle diameter D_(N4) of colloidal silica, which is determined by the laser diffraction scattering method, is preferably in the range of 5 to 300 nm, more preferably in the range of 5 to 200 nm, and most preferably in the range of 5 to 150 nm. When silicon dioxide is fumed silica, the mean particle diameter D_(SA) of fumed silica is preferably in the range of 10 to 300 nm, more preferably in the range of 10 to 200 nm, and most preferably in the range of 10 to 120 nm. The mean particle diameter D_(N4) of fumed silica is preferably in the range of 30 to 500 nm, more preferably in the range of 40 to 400 nm, and most preferably in the range of 50 to 300 nm. When the mean particle diameter D_(SA) or D_(N4) of colloidal silica is too small, or when the mean particle diameter D_(SA) or D_(N4) of fumed silica is too small, it is highly possible that a sufficiently high stock removal rate will not be obtained. When the mean particle diameter D_(SA) or D_(N4) of colloidal silica is too large, or when the mean particle diameter D_(SA) or D_(N4) of fumed silica is too large, it is highly possible that the surface roughness of the polished glass substrate will become large, or scratching will occur on the surface of the polished glass substrate.

The content of silicon dioxide in the polishing composition is preferably in the range of 0.1 to 50 mass %, more preferably in the range of 1 to 40 mass %, and most preferably in the range of 3 to 30 mass %. When the content of silicon dioxide is less than 0.1 mass %, a sufficiently high stock removal rate might not be obtained, or polishing the glass substrate may become difficult due to high polishing resistance. When the content of silicon dioxide exceeds 50 mass %, the viscosity of the polishing composition excessively increases to make the polishing composition apt to gelate, leading to reduction in handleability of the polishing composition.

The alkaline compound serves as a polishing accelerator for accelerating mechanical polishing by silicon dioxide. The reason why the alkaline compound accelerates mechanical polishing is presumably that the alkaline compound acts on the surface of silicon dioxide for activation, thereby increasing the mechanical polishing force of silicon dioxide. The alkaline compound also corrodes or etches the glass substrate surface, as a secondary action, to chemically polish the glass substrate surface. The chemical polishing action of the alkaline compound is weaker than the mechanical polishing action of silicon dioxide.

The alkaline compound may be alkali metal salt, alkaline earth metal salt, or ammonium salt of one acid selected from carbonic acid, phosphoric acid, pyrophosphoric acid (diphosphoric acid), citric acid, gluconic acid, succinic acid, acetic acid, oxalic acid, tartaric acid, sorbic acid, and nitric acid. Alternatively, the alkaline compound may be ferricyanide, fluoride, or hydroxide of one kind selected from alkali metal, alkaline earth metal, and ammonia. Further alternatively, the alkaline compound may be quaternary ammonium hydroxide. Alkali metal in the alkaline compound may be potassium, lithium, and sodium. Alkaline earth metal in the alkaline compound may be calcium. Among them, alkali metal salt, alkaline earth metal salt, or ammonium salt of one acid selected from carbonic acid, phosphoric acid, and pyrophosphoric acid are preferable, since the stock removal rate is strongly improved.

Specifically, examples of the alkaline compound may include ammonium carbonate, potassium carbonate, sodium carbonate, ammonium hydrogen carbonate, potassium hydrogen carbonate, sodium hydrogen carbonate, ammonium phosphate, potassium phosphate, sodium phosphate, ammonium hydrogen phosphate such as diammonium hydrogen phosphate, potassium hydrogen phosphate such as dipotassium hydrogen phosphate, sodium hydrogen phosphate such as disodium hydrogen phosphate, potassium pyrophosphate, sodium pyrophosphate, potassium citrate, potassium hydrogen citrate such as dipotassium hydrogen citrate, potassium gluconate, potassium succinate, ammonium acetate, potassium oxalate, ammonium hydrogen oxalate, ammonium tartrate, potassium tartrate, ammonium hydrogen tartrate, potassium sodium tartrate, potassium sorbate, calcium nitrate, potassium ferricyanide, ammonium fluoride, potassium fluoride, calcium fluoride, potassium hydroxide, ammonium hydroxide, and tetramethyl ammonium hydroxide (TMAH). Among them, ammonium carbonate, potassium carbonate, sodium carbonate, ammonium hydrogen carbonate, potassium hydrogen carbonate, sodium hydrogen carbonate, ammonium phosphate, potassium phosphate, sodium phosphate, ammonium hydrogen phosphate, potassium hydrogen phosphate, and sodium hydrogen phosphate are preferable, since the stock removal rate is strongly improved. One or more alkaline compounds may be contained in the polishing composition.

The content of the alkaline compound in the polishing composition is preferably in the range of 0.05 to 10 mass %, more preferably in the range of 0.1 to 8 mass %, and most preferably in the range of 0.3 to 5 mass %. When the content of the alkaline compound is less than 0.05 mass %, it is highly possible that a sufficiently high stock removal rate will not be obtained because the alkaline compound weakly acts to chemically polish the glass substrate surface. When the content of the alkaline compound exceeds 10 mass %, the viscosity of the polishing composition excessively increases to make the polishing composition apt to gelate, which is uneconomical and further increases the possibility of producing roughness on the surface of the polished glass substrate.

Water serves to dissolve or disperse ingredients other than water of the polishing composition. Water preferably contains as little impurities as possible so as to avoid inhibiting the actions of other ingredients. Specifically, pure water or ultrapure water, obtained by removing impurity ions with an ion-exchange resin and then contaminants through a filter, or distilled water, is preferable.

The polishing composition may further contain an oxidizing agent. The oxidizing agent serves as a polishing accelerator for accelerating mechanical polishing by silicon dioxide by means of oxidizing the glass substrate surface. The oxidizing agent may be aqueous solution of hydrogen peroxide (31 mass %), or may be alkali metal salt, such as potassium salt and sodium salt, or ammonium salt of one acid selected from persulfuric acid, chloric acid, perchloric acid, periodic acid, and bromic acid. Specifically, examples of the oxidizing agent may include hydrogen peroxide, ammonium persulfate, potassium chlorate, potassium perchlorate, sodium perchlorate, potassium periodate, sodium periodate, potassium bromate, and sodium bromate. Among them, hydrogen peroxide is preferable, since hydrogen peroxide strongly act to accelerate mechanical polishing by silicon dioxide. One or more oxidizing agents may be contained in the polishing composition.

The content of the oxidizing agent in the polishing composition is preferably in the range of 0.005 to 10 mass %, more preferably in the range of 0.01 to 8 mass %, and most preferably in the range of 0.03 to 5 mass %. When the content of the oxidizing agent is less than 0.005 mass %, it is highly possible that a sufficiently high stock removal rate will not be obtained because the oxidizing agent weakly acts to accelerate mechanical polishing by silicon dioxide. When the content of the oxidizing agent exceeds 10 mass %, the viscosity of the polishing composition excessively increases to make the polishing composition apt to gelate, which is uneconomical and further increases the possibility of producing roughness on the surface of the polished glass substrate.

The polishing composition may further contain a chelating agent, a surfactant, a preservative, or the like according to need.

The polishing composition is prepared by mixing ingredients, other than water, with water. In the mixing, a blade-type agitator or an ultrasonic disperser may be used. There is no limitation to the order of mixing the ingredients, other than water, into water.

A polishing composition according to the present embodiment may be provided for use after dilution with water, or without dilution. When the polishing composition is diluted with water, the dilution ratio (ratio by volume) is preferably not more than 50 times, more preferably not more than 20 times, and most preferably not more than 10 times. When the dilution rate exceeds 50 times, the content of silicon dioxide and the alkaline compound in the polishing composition after dilution might become excessively low, resulting in failure to obtain a sufficiently high stock removal rate.

The case where a glass substrate is polished by conducting the two-stage polishing process consisting of the rough polishing step and the superfine polishing step will be described. First, in the rough polishing step, the surface of a glass substrate is relatively roughly polished using polishing slurry containing cerium oxide. Next, in the superfine polishing step as the final polishing step, the glass substrate surface is superfinely polished using the polishing composition according to the present embodiment. In the superfine polishing, in a state where the glass substrate attached to a polishing head is kept pressed to a polishing pad on a turntable at constant pressure, the polishing composition is provided to the surface of the polishing pad while the polishing head and the turntable are rotated.

It is to be noted that a glass substrate may be polished in a single-staged polishing process using a polishing composition according to the present embodiment, in place of a multi-stage polishing process.

The present embodiment has the following advantages.

A polishing composition according to the present embodiment contains silicon dioxide as an abrasive. This reduces the surface roughness of the polished glass substrate, as compared to a polishing composition containing cerium oxide as an abrasive. Presumably, this is attributed to the fact that the primary particle of cerium oxide has an irregular form whereas the primary particle of silicon dioxide has a spherical form. Namely, it is presumed that, with the primary particle in spherical form, silicon dioxide is capable of polishing the glass substrate surface more finely than cerium oxide, thereby to reduce surface roughness of the polished glass substrate.

Moreover, silicon dioxide has lower reactivity to a glass substrate material than cerium oxide. For this reason, silicon dioxide attached to the glass substrate is readily removed by cleaning from the glass substrate without reacting with a glass substrate material and sticking to the glass substrate surface. It can therefore be said that a polishing composition according to the present embodiment has the property of being readily cleaned off from the polishing surface.

Furthermore, silicon dioxide has greater resistance to agglomeration and higher dispersibility in the polishing composition than cerium oxide (cf. later-described Examples 1 to 29 and Comparative Examples 4, 5). It can therefore be said that a polishing composition according to the present embodiment also contains an adhesive having good dispersibility.

The alkaline compound in the polishing composition acts to accelerate mechanical polishing by silicon dioxide as well as to chemically polish the glass substrate surface. By such actions of the alkaline compound, the ability of the polishing composition to polish the glass substrate improves, which leads to improvement in stock removal rate. It should be noted that, while the alkaline compound contributes to improvement in stock removal rate by means of activation of the silicon dioxide surface and etching of the glass substrate surface, it is not considered to act to oxidize the glass substrate surface to be made brittle.

Next, examples and comparative examples of the present invention will be described.

In each of Examples 1 to 29, an abrasive and an alkaline compound were mixed with water, and thereafter, oxidizing agent was further added thereto as necessary, so as to prepare a stock solution of a polishing composition. In each of Comparative Examples 1 to 5, an abrasive was mixed with water, and thereafter, oxidizing agent was further added thereto as necessary, so as to prepare a stock solution of a polishing composition. The kinds and contents of abrasives, alkaline compounds, and oxidizing agents used are as shown in Table 1.

Each stock solution according to Examples 1 to 29 and Comparative examples 1 to 5 was diluted with ultrapure water, so that the final volume could become 10 times the initial volume, thereby preparing a polishing composition. Using the thus obtained polishing composition according to each of Examples 1 to 29 and Comparative examples 1 to 5, the surface of a glass substrate was polished under the polishing conditions described below. Herein, the mass of each glass substrate before and after polishing was measured, and a stock removal rate was then calculated by the below-mentioned formula. Based on the obtained stock removal rate, each of the polishing compositions was rated on a scale from one to four: (1) Very Good; (2) Good; (3) Slightly Poor; and (4) Poor. Specifically, the polishing composition was rated very good when the stock removal rate was not less than 0.05 μm/minute; it was rated good when the stock removal rate was not less than 0.03 μm/minute and less than 0.05 μm/minute; it was rated slightly poor when the stock removal rate was not less than 0.02 μm/minute and less than 0.03 μm/minute; it was rated poor when the stock removal rate was less than 0.02 μm/minute. These rating results are shown in the column entitled “Stock removal rate” in Table 1.

<Polishing Condition>

Polishing machine: single-sided polishing machine 15″φ (3 pieces/plate), manufactured by Engis Corporation (Japan).

Material to be polished: 2.5-inch (external diameter: 63.5 mm) glass substrate obtained by roughly polishing the surface of reinforced glass, using polishing slurry containing cerium oxide, so as to have a surface roughness Ra of 0.8 nm.

Polishing pad: Suede type polishing pad “Belatrix N0058,” manufactured by Kanebo, Ltd.

Polishing pressure: 100 g/cm²(=9.8 kPa)

Turntable rotation speed: 102 rpm

Polishing composition supplied speed: 50 ml/minute

Polishing time: 20 minutes

<Calculation Formula> Stock removal rate [μm/minute]=(Difference in mass [g] of glass substrate before/after polishing÷(30.02625 [cm²]×2.52 [g/cm³])×10000 [μm/cm])÷polishing time [minute]

The polished glass substrate was subjected to scrub cleaning for 30 seconds and megasonic cleaning for 45 seconds, and then spin drying for 180 seconds. Thereafter, the surface condition of the glass substrate was observed with an atomic force microscope “NanoScope IIIa Dimension 3000” (scan area: 10 μm×10 μm, scan rate: 1.00 Hz, sample lines: 256), manufactured by Digital Instruments Inc. Based on the observed number of adherents to the glass substrate surface, each of the polishing compositions was rated on a scale from one to four: (1) Very Good; (2) Good; (3) Slightly Poor; and (4) Poor. Specifically, the polishing composition was rated very good when the observed number of adherents to the glass substrate surface was zero; it was rated good when the number of adherents was less than 3; it was rated slightly poor when the number of adherents was not less than 3 and less than 5; it was rated poor when the number of adherents was not less than 5. These rating results are shown in the column entitled “Ease of cleaning” in Table 1.

The surface roughness Ra of the glass substrate after spin drying was measured with an atomic force microscope “NanoScope IIIa Dimension 3000” (scan area: 10 μm×10 μm, scan rate: 1.00 Hz, sample lines: 256, off-line filter: flatten auto order-2). Based on the measured surface roughness Ra of the glass substrate, each of the polishing compositions was rated on a scale from one to four: (1) Very Good; (2) Good; (3) Slightly Poor; and (4) Poor. Specifically, the polishing composition was rated very good when the surface roughness Ra was less than 0.2 nm; it was rated good when the surface roughness Ra was not less than 0.2 nm and less than 0.25 nm: it was rated slightly poor when the surface roughness was not less than 0.25 nm and less than 0.3 nm; it was rated poor when the surface roughness Ra was not less than 0.3 nm. These rating results are shown in the column entitled “Surface roughness” in Table 1.

Each of the polishing compositions according to Examples 1 to 29 and Comparative Examples 1 to 5 was put into a calorimetric tube having an inner diameter of 2.5 cm, and allowed to stand there for one hour. Thereafter, the height of a deposit produced in the polishing composition in each calorimetric tube was measured. Based on the measured height of the deposit, each of the polishing compositions was rated on a scale from one to four: (1) Very Good; (2) Good; (3) Slightly Poor; and (4) Poor. Specifically, the polishing composition was rated very good when the height of the deposit was less than 1 cm; it was rated good when the height of the deposit was not less than 1 cm and less than 2 cm: it was rated slightly poor when the height of the deposit was not less than 2 cm and less than 3 cm; it was rated poor when the height of the deposit was not less than 3 cm. Those rating results are shown in the column entitled “Dispersibility” in Table 1.

Based on the above results of the ratings for the four items: Stock removal rate, Ease of cleaning, Surface roughness, and Dispersibility, each of the polishing compositions was comprehensively rated on a scale from one to four: (1) Very Good; (2) Good; (3) Slightly Poor; and (4) Poor. Specifically, 5 points, 3 points, 1 point and 0 point were given for Very Good, Good, Slightly Poor and Poor, respectively, and the total rating points obtained by each polishing composition was accordingly calculated. A polishing composition was rated very good when the total rating points for the four items was 20, it was rated good when the total rating points was 16 to 19, it was rated slightly poor when the total rating points was 10 to 15, and it was rated poor when the total rating points was 9 or less. These rating results are shown in the column entitled “Comprehensive rating” in Table 1. TABLE 1 Abrasive Alkaline compound Oxidizing agent Stock Ease of Surface Comprehensive [mass percentage] [mass percentage] [mass percentage] removal rate cleaning roughness Dispersibility rating Ex. 1 colloidal silica*¹ potassium carbonate hydrogen peroxide 1 1 1 1 1 25% 2% 2% Ex. 2 colloidal silica*¹ potassium carbonate hydrogen peroxide 1 1 1 1 1 25% 5% 2% Ex. 3 colloidal silica*¹ potassium carbonate hydrogen peroxide 2 1 1 1 2 25% 0.2% 2% Ex. 4 colloidal silica*¹ potassium carbonate hydrogen peroxide 3 1 1 1 2 25% 0.01% 2% Ex. 5 colloidal silica*¹ potassium carbonate hydrogen peroxide 3 1 1 1 2 5% 2% 2% Ex. 6 colloidal silica*¹ potassium carbonate hydrogen peroxide 2 1 1 1 2 10% 2% 2% Ex. 7 colloidal silica*¹ potassium carbonate hydrogen peroxide 1 1 1 1 1 40% 2% 2% Ex. 8 colloidal silica*¹ potassium carbonate — 2 1 1 1 2 25% 2% Ex. 9 colloidal silica*¹ potassium carbonate hydrogen peroxide 2 1 1 1 2 25% 2% 0.01% Ex. 10 colloidal silica*¹ potassium carbonate hydrogen peroxide 1 1 1 1 1 25% 2% 10% Ex. 11 fumed silica*¹ potassium carbonate hydrogen peroxide 1 1 3 1 2 25% 2% 2% Ex. 12 colloidal silica*¹ disodium hydrogen phosphate hydrogen peroxide 1 1 1 1 1 25% 2% 2% Ex. 13 colloidal silica*¹ trisodium phosphate hydrogen peroxide 1 1 1 1 1 25% 2% 2% Ex. 14 colloidal silica*¹ potassium hydrogen carbonate hydrogen peroxide 1 1 1 1 1 25% 2% 2% Ex. 15 colloidal silica*¹ potassium hydroxide hydrogen peroxide 2 1 1 1 2 25% 2% 2% Ex. 16 colloidal silica*¹ potassium sodium tartrate hydrogen peroxide 2 1 1 1 2 25% 2% 2% Ex. 17 colloidal silica*¹ tripotassium phosphate hydrogen peroxide 2 1 1 1 2 25% 2% 2% Ex. 18 colloidal silica*¹ potassium pyrophosphate hydrogen peroxide 2 1 1 1 2 25% 2% 2% Ex. 19 colloidal silica*¹ tripotassium citrate hydrogen peroxide 2 1 1 1 2 25% 2% 2% Ex. 20 colloidal silica*¹ lithium hydroxide hydrogen peroxide 2 1 1 1 2 25% 2% 2% Ex. 21 colloidal silica*¹ sodium hydroxide hydrogen peroxide 2 1 1 1 2 25% 2% 2% Ex. 22 colloidal silica*¹ ammonium hydroxide hydrogen peroxide 3 1 1 1 2 25% 2% 2% Ex. 23 colloidal silica*¹ TMAH hydrogen peroxide 3 1 1 1 2 25% 2% 2% Ex. 24 colloidal silica*¹ calcium nitrate hydrogen peroxide 3 1 1 1 2 25% 2% 2% Ex. 25 colloidal silica*¹ potassium carbonate hydrogen peroxide 2 1 1 1 2 25% 2% 2% Ex. 26 colloidal silica*¹ potassium carbonate sodium perchlorate 2 1 1 1 2 25% 2% 2% Ex. 27 colloidal silica*¹ potassium carbonate sodium bromate 2 1 1 1 2 25% 2% 2% Ex. 28 colloidal silica*² potassium carbonate hydrogen peroxide 2 1 1 1 2 25% 2% 2% Ex. 29 fumed silica*² potassium carbonate hydrogen peroxide 1 1 3 1 2 25% 2% 2% C. Ex. 1 colloidal silica*¹ — — 4 1 1 1 3 25% C. Ex. 2 colloidal silica*¹ — hydrogen peroxide 4 1 1 1 3 25% 2% C. Ex. 3 fumed silica*¹ — — 2 1 3 1 3 25% C. Ex. 4 cerium oxide — — 1 4 4 4 4 25% C. Ex. 5 iron oxide — — 2 3 3 4 4 25%

In the “Abrasive” column in Table 1:

“colloidal silica^(*1)” is colloidal silica having a mean particle size D_(SA) of 80 nm and a mean particle size D_(N4) of 80 nm;

“colloidal silica^(*2)” is colloidal silica having a mean particle size D_(SA) of 20 nm and a mean particle size D_(N4) of 40 nm;

“fumed silica^(*1)” is fumed silica having a mean particle size D_(SA) of 30 nm and a mean particle size D_(N4) of 170 nm;

“fumed silica^(*2)” is fumed silica having a mean particle size D_(SA) of 20 nm and a mean particle size D_(N4) of 140 nm;

“cerium oxide” is cerium oxide (Ce₂O₃) having a mean particle size D₅₀ of 450 nm; and

“iron oxide” is iron oxide (α-Fe₂O₃) having a mean particle size D₅₀ of 450 nm.

The mean particle size D₅₀ of cerium oxide and iron oxide were measured using a Coulter counter “LS-230”, manufactured by Beckman Coulter Inc.

In the “Oxidizing agent” column in Table 1, “hydrogen peroxide” is aqueous solution of hydrogen peroxide (31 mass %).

As shown in Table 1, each of the polishing compositions according to Examples 1 to 29 was not rated as poor for any rating item, and was rated as either very good or good for the “Comprehensive rating”. This result suggests that the polishing compositions according to Examples 1 to 29 are useful in applications for polishing a glass substrate. It was found from the rating results of the polishing compositions according to Examples 1 and 5 to 7 that the stock removal rate improves, in particular, by setting the content of silicon dioxide (abrasive) to not less than 25 mass %, and more specifically in the range of 25 to 40 mass %. It was also found from the rating results of the polishing compositions according to Examples 1 to 4 that the stock removal rate improves, in particular, by setting the content of alkaline compound to not less than 2 mass %, and more specifically in the range of 2 to 5 mass %. It was further found from the rating results of the polishing compositions according to Examples 1, 9, and 10 that the stock removal rate improves, in particular, by setting the content of the acid to not less than 2 mass %, and more specifically in the range of 2 to 10 mass %.

The present examples and embodiments are to be considered as illustrative and not restrictive and the invention is not to be limited to the details given herein, but may be modified within the scope and equivalence of the appended claims. 

1. (canceled)
 2. (canceled)
 3. (canceled)
 4. (canceled)
 5. (canceled)
 6. (canceled)
 7. (canceled)
 8. (canceled)
 9. (canceled)
 10. The method according to claim 18, wherein the alkaline compound is ammonium carbonate, potassium carbonate, sodium carbonate, ammonium hydrogen carbonate, potassium hydrogen carbonate, sodium hydrogen carbonate, ammonium phosphate, potassium phosphate, sodium phosphate, ammonium hydrogen phosphate, potassium hydrogen phosphate, sodium hydrogen phosphate, potassium pyrophosphate, sodium pyrophosphate, potassium citrate, potassium hydrogen citrate, potassium gluconate, potassium succinate, ammonium acetate, potassium oxalate, ammonium hydrogen oxalate, ammonium tartrate, potassium tartrate, ammonium hydrogen tartrate, potassium sodium tartrate, potassium sorbate, calcium nitrate, potassium ferricyanide, ammonium fluoride, potassium fluoride, calcium fluoride, potassium hydroxide, ammonium hydroxide, or tetramethyl ammonium hydroxide.
 11. (canceled)
 12. (canceled)
 13. The method according to claim 18, further comprising an oxidizing agent.
 14. The method according to claim 13, wherein the oxidizing agent is hydrogen peroxide, ammonium persulfate, potassium chlorate, potassium perchlorate, sodium perchlorate, potassium periodate, sodium periodate, potassium bromate, or sodium bromate
 15. (canceled)
 16. (canceled)
 17. (canceled)
 18. A method for polishing a glass substrate, the method comprising: preparing a polishing composition comprising silicon dioxide, an alkaline compound, and water; and polishing the surface of a glass substrate, using the prepared polishing composition.
 19. The method for polishing a glass substrate according to claim 18, wherein said polishing the surface of a glass substrate comprises: preliminarily polishing the surface of the glass substrate; and finish-polishing the surface of the preliminarily polished glass substrate, in which the polishing composition is used in the finish-polishing of the surface of the preliminarily polished glass substrate.
 20. The method for polishing a glass substrate according to claim 18, wherein said preparing a polishing composition comprises diluting the polishing composition with water. 